Use of Pc Based Mathematics Software in the Undergraduate Curriculum
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11fi-d.. •., ~..____:_c_u_r_r,___· c ___ u _l___u _m_____ _____) USE OF PC BASED MATHEMATICS SOFTWARE IN THE UNDERGRADUATE CURRICULUM JOSEPH M. SLAUGHTER, JAMES N. PETERSEN, RICHARD L. ZOLLARS it had to be a general purpose package, capable of all Washington State University the calculations (solving sets oflinear and/or nonlin Pullman, WA 99164-2710 ear equations, iterative calculations, vector/matrix manipulations, curve fitting, simple statistics, re ith the advent of the personal computer, many gression) which are typically encountered by a stu W software packages have been developed which dent progressing through our curriculum. For this minimize the required programming, thus allowing reason, spreadsheet programs were not included the user to concentrate on understanding the prob since, although many typical problems can be solved, lem rather than on debugging. This is very desirable the structure of the program is not optimal for all from an educational point of view. However, if stu of the calculations (solution ofODE's, sets of nonlin dents are required to learn the use of many different ear equations, etc.). Likewise, such packages as packages, any advantages gained by reducing pro Matlab 141 and GAUSS 151 , which concentrate on gramming requirements are offset by increasing the matrix manipulations, were not included. time spent learning how to use the various pack Second, the program had to be capable of opera ages. In this article we will describe the experiences tion on the PC's available in our department of one of our undergraduate students in learning 111 (IBM PC/XT or AT's, or compatibles), which are and using three such programs (MathCAD , Point also typical of those owned by the students. Thus, Five 121, TK Solver Plus 131) which we have examined many of the symbolic manipulators (Macsyma 161) for incorporation into our curriculum. were not considered. Obviously, there are more packages available than Finally, we wanted the packages to be priced the three cited above, but we sought to find a single within the grasp of a typical student so that they package which met all of the following criteria. First, might be purchased for use away from the academic setting. Of the three packages evaluated, both Joseph Slaughter is a graduate student in chemical MathCAD and TK Solver Plus are available as stu engineering at Washington State University. He re ceived a BS degree in chemical engineering and a BA dent versions for approximately $50, while Point degree in foreign languages and literatures, French, Five can be site licensed for a reasonable fee. There from Washington State University in 1989. His current are also a number of packages available with inter research is in the area of bioseparations using large scale electrophoresis. faces and structures very similar to TK Solver Plus, such as Eureka 171 and FORMULA/ONE 181 • Of this group, however, only TK Solver Plus was evaluated, James N. Petersen is currently an associate professor Richard L. Zollars is a professor of chemical engi of chemical engineering at Washington State Univer neering at Washington State University. He received sity. He received his BS degree from Montana State his BChE (1968) from the University of Minnesota University in 1976 and his PhD from Iowa State Univer and his MS (1972) and PhD (1974) from the Univer sity in 1979. His current research interests are in the sity of Colorado. His current research interests in adsorption of heavy metals from aqueous streams by clude adsorption, colloidal and interfacial phenom biological materials, and modeling and on-line optimi ena, and bioseparations. zation of biological processes. © Copyright ChE Division ASEE 1991 54 Chemical Engineering Education In this article we will describe the experiences of one of our undergraduate students in learning and using three programs (Math CAD, Point Five, and TK Solver Plus) which we have examined for incorporation into our curriculum. due to its availability in a student version and its countered, help could be found either in the user's greater power. guide or with the on-line help facility. One of the strongest characteristics for use in education is its All of the packages evaluated can be run on IBM format. Graphically created symbols are used in PC/XT's or compatibles with no more than 512K, stead of function names, i.e., ✓ ( arg ) instead of two 5 1/4" floppy disk drives, a graphics card, and a sqrt(arg), as shown in Figure 1. Also, eighteen com dot matrix printer. For this evaluation we used an monly used Greek letters are available for use in the IBM PS/2 Model 50Z personal computer equipped equations and text. These symbols make it easier for with a 80287 math co-processor. Feature-by-feature the user to find errors and to create a readable comparisons of many of these software packages have report. appeared 19•111 , but this type of comparison does not indicate how easily the package can be learned and The free-format style of the problem files makes used, nor its ability to easily solve typical chemical editing quite easy, much like erasing an error on engineering problems and create a readable report a paper scratchpad. However, moving about in (such as would be required if a student used the MathCAD can become tedious in large files since the package to solve homework problems). Therefore, maximum cursor movement is either 80% of a page one of our senior chemical engineering students (J . or to the beginning or end of the current region. Slaughter) was asked to solve typical homework Moving through the file is slowed even further if problems from a number of areas (thermodynamics MathCAD is in its automatic calculation mode. This 1121 , unit operations 1!3J, reactor design 1141 , kinetics 115 1, latter problem can be overcome by switching to the and numerical analysis 1161 ) using MathCAD, TK manual calculation mode. MathCAD can also write Solver Plus, and Point Five. Each program was then and read ASCII files so that data created from other evaluated for its utility. software can be analyzed. MATHCAD MathCAD solves simultaneous equations (linear and non-linear) using a solve block technique (see MathCAD is a free-format scientific scratchpad Figure 2). This technique is initiated by guessing a supporting 69 built-in functions and 29 symbolic op value for the unknown, entering the equation to be erators. It comes on two disks with a well-written solved by using a "given" command, and requesting user's guide and a MathCAD reference booklet. Af the solution by using a "find" command. If the con ter reading the first three chapters of the user's vergence criteria is not met, MathCAD will supply a guide we felt fairly confident about setting up solu message to that effect, and the "find" command can tions to typical problems. When difficulties were en- be replaced by a "minerr" command to find the result 1 - •.6 Ca l cula tes the Re!Jno lds nu111b er using Gue ss . .. intcr atiuc ualuc s f o r t he f ann ing fr iction . 1 . 07 10 Re =-- 1 f. g i ven . 1 G ~ Fl f.'.. :. ' n' r I ka : = find[ka] n = 3 2 3 13 "' - 1 . 001 ~----------------~ k = 6 .683 -10 ·sec "<--- - ------- ns" 100 Re ,l e+007. Figure 1 Figu re 2 FIGURE 1. MathCAD screen showing features such as FIGURE 2. Example of Math CAD use of a solve symbol opera tors and imbedded graphics. block and units. Winter 1990 55 with the smallest error. The results obtained using the base units, checks for compatibility and gives the "minerr" are good estimates which can then be used results in the base units. The user is able to change as new guess values. to any defined unit by simply entering the desired unit. Not only does this feature provide a means of MathCAD performs iterative calculations using detecting errors, but it also makes the report much vector notation and an iteration counter (range vari more readable (see Figure 2). MathCAD provides able), as shown in Figure 3. Only one equation may three files (for mks, cgs, and US customary units) appear inside this iteration loop, but multiple func that contain most of the desired unit conversions. tions may be used. In Figure 3, for example, a user defined function called "gradf(s,y)" is defined by us Perhaps MathCAD's strongest point is the reada ing the built-in derivative function. Other user-de bility of its output, as shown in Figures 1 through 4. fined functions [H(x,y), s(x,y), and A(x,y)J are subse The graphical representation of operators, ability to quently defined using "gradf', and all of the func mix text, plots, and calculations, and the inclusion of tions are combined into a single equation which is units on the calculations makes the output appear used in the calculation. much as it would if the user were using a paper and pencil. Indeed, one does not need to know much Graphs can be created very easily in MathCAD about MathCAD in order to be able to read the out and can be imbedded into the report. Graphs can be put. The only noticeable idiosyncracy in the output is formatted for size, type (linear, semi-log, or log-log), the use of the symbols ":=" and "=". MathCAD re- and number of subdivisions for each axis using six different symbols with or without a connecting line. One graphing feature that we found desirable d - rcx .y> was the ability to define the x-axis with more than dx .. gradient of f(x , y) gradf(x,y) : = d one variable (neither Point Five nor TK Solver Plus - rcx,y) were able to do this), as shown in Figure 4.